3. MATERIALES Y MÉTODOS 29
3.1 Planta piloto 29
4.3.1 General features of Macro-PDM
Macro-PDM, an adaptation of the Probability Distributed Moisture model (PDM) (Moore, 1985, 2007), was developed to be applied across large geographical domains, such that its parameters could be defined a-priori according to the spatial
distribution of vegetation (specifically forest and grass) and soil types. Like PDM, Macro-PDM takes a conceptual water balance approach to rainfall-runoff modelling, based on a soil moisture accounting procedure, and works on a daily time step to transform inputs of precipitation, potential evaporation (PE) and temperature into estimates of runoff. The application of PDM within Macro-PDM has been described previously by others (e.g. Arnell, 1999b; Reynard et al., 1997) and, because it was
applied without modification in this study, a more detailed description of its treatment of the different runoff-generating processes within a grid cell is provided for completeness in Appendix A.
A schematic of Macro-PDM is shown in Figure 4.2. As with many MHMs, Macro- PDM is a deterministic, grid-based conceptual rainfall-runoff model that requires, as input, gridded driving- and antecedent-data and various model parameter settings to produce, as output, gridded estimates of runoff. Macro-PDM uses a regular rectilinear grid in which all grid cells are rectangles whose size (resolution) can be modified as
92 necessary, usually, according to the resolution of available driving- or antecedent data. Grid cell resolutions of previous applications range from 10 km x 10 km (Rees
et al., 1997) to 0.5º x 0.5º latitude-longitude (e.g. Reynard et al., 1997; Meigh et al.,
1999). Driving data are the meteorological inputs that are necessary to “drive” the model. Antecedent data are data that describe the initial physical characteristics of each grid-cell (e.g. soil type, land-cover, elevation). A requirement of the model is that all input data must be available, or prepared, at the same spatial resolution as the model. As Macro-PDM works on a daily time-step, the driving data must also be converted to daily. Details on how the available data were assessed, prepared and applied to the model are provided in Chapter 5 (Model Application).
The model comprises many sub-components (modules) that individually characterise key physical processes acting within a grid cell and which interact to ultimately provide daily estimates of runoff for every grid cell, the model’s primary output. These daily estimates can then be aggregated at run-time to provide the required long- term (i.e. whole period of the model run) or interim (e.g. decadal) averages of annual- or seasonal-runoff for every grid cell.
Macro-PDM considers each grid-cell as a discrete unit and does not consider the routing of runoff between neighbouring cells. To overcome this limitation, the physical, hydraulic routing of runoff between cells that is required to derive estimates of river flow at specific points along the river network is carried out as a subsequent, post-processing, activity independently of the model.
4.3.2 Snow- and ice-melt modelling within Macro-PDM
Macro-PDM’s treatment of snow and ice is particularly relevant to this study’s application of the model in the Himalaya. Earlier versions of the model assumed input variables to be uniformly distributed across the cell. However, the model was adapted in 2001 for an application in mountainous Central Asia (Tate and Meigh, 2001), to account for altitudinal variations in the three climate input variables. Cells having a maximum elevation of 2000 m or higher were declared “mountain” cells.
93 Figure 4.3 A schematic of the macro-scale hydrological model, Macro-PDM, showing the various inputs to, and outputs from, the model and its key modules (* shows those that were new or significantly modified during this study)
Macro-PDM Gridded driving data P (mm) PE (mm) T (˚C) Gridded output (runoff) Q (mm) Model parameters
e.g. lapse rate, DDFsnow/ice, etc.
Point flow
Q (m3/s)
Gridded antecedent data
DTM, Land-cover, Soils, Glaciers
Interception Evapo- transpiration Soil moisture P & T lapse rates* Groundwater storage Runoff generation Snowpack- snowmelt* Glacier-melt* Post processed
94 Every mountain cell is subdivided (discretized) into a number of discrete elevation bands of equal-height between the vertical extremes of the cell. The distribution of cell area between bands (the cell hypsometry) is determined according to the Pareto distribution, such that F(zi), the proportion of the cell below the minimum elevation of any band, zi, is expressed by:
(
)
n i i f z z F( )=1− 1− ( ) …(4.2a) where ) ( 1 mean z f n= and min max min ) ( z z z z z f mean mean − − = …(4.2b)and zmean, zmin and zmax are the mean, minimum and maximum cell elevations respectively, values that usually can be obtained by overlaying the model grid onto a suitable digital elevation model .
The area, Ai, of any band, i, can thus be calculated as:
= − ...(4.3)
where A is the total cell area, in km2, and i = 1 is the lowermost elevation band.
With the daily temperature for the cell, Tmean, (ºC) assumed to apply at the cell’s mean elevation, zmean, the daily temperature in each elevation band, Ti, is calculated according to temperature lapse rate, as follows:
= + − …(4.4)
where zmid is the mid-elevation of the band and α is the temperature lapse rate (ºC/km).
95 Daily precipitation (mm) and potential evaporation (mm) are also allowed to vary with elevation in so-called mountain cells. A simple model is applied to account for orographic increases in precipitation (Equation 4.5), such that the daily precipitation in each elevation band, Pi, increases by a certain percentage (∆P, %/100 m) of the cell daily precipitation, P, at all elevations above the cell mean elevation.
=
where ≤ 1 + ∆$%&'($%)*+ ,,⁄ where >
/ ...(4.5)
PE can similarly be adjusted (Equation 4.6), reducing exponentially relative to the mean cell elevation and according to a PE lapse rate, ∆PE (/km).
=
where ≤ ∙ 12+ ∆34∙$%&'($%)*+/6777 where >
/
...(4.6)
Precipitation is considered to reach the ground as snow whenever the band’s daily temperature is below a certain threshold temperature, Tsnow. A snowpack-snowmelt model that couples with the PDM (Bell and Moore, 1999) is applied whenever snow is present in an elevation band. The model represents the accumulation and depletion of the snowpack and the snowmelt contribution to runoff in each elevation band. It uses a temperature index (degree-day) approach to calculate snowmelt and conceptualizes the snowpack (snow storage) as a dry-(snow) store and a wet-(snow) store in series. Any new snow in a band added to the band’s dry-store. The wet-store receives water directly as rainfall and, whenever the daily temperature for the band is above a melt threshold (Tmelt), as snowmelt from the dry-store, at the constant rate of the degree-day-factor for snow, DDFsnow. The rate at which melt-water is “released” from the snowpack depends on the wetness of the wet-store, as represented by a model parameter, Sc, the critical liquid water capacity. Sc is the proportion of the wet- store above which fast drainage of melt-water occurs at a rate k2. The water content
below Sc drains at a slower rate of k1.The storage time parameters k1 and k2 have units of inverse time. Typical values for snowpack model parameters are shown in Table 4.2, at the end of the chapter.
96 A further key innovation of the 2001 model was the assumption that an inexhaustible supply of permanent snow and ice is available at all elevation bands above 4000 m, with melt-water released from such elevation bands at the same constant rate per degree-day, DDFsnow, whenever the daily temperature is above melt threshold, Tmelt.
Whenever snow or ice are present in an elevation band, the daily melt-water constitute the effective precipitation input to the daily PDM runoff calculations that are applied in the band. The daily cell runoff, Qt, finally is calculated as the area-weighted total of the daily runoff from all elevation bands, as follows:
= 8.
:
;/ ...(4.7)
Where Aiis the area of band, i (i = 1,2 ... n, the number of bands), qi, the daily runoff from the band, and A is the cell area.